New Proofs of K\"onigs Theorem

TL;DR

This paper presents four new elementary proofs of K"onig's theorem, which characterizes bipartite graphs by the absence of odd cycles, offering simpler approaches to this fundamental graph theory result.

Contribution

The paper introduces four novel, elementary proofs of K"onig's theorem, enhancing understanding and accessibility of this key graph theory concept.

Findings

Four new elementary proofs of K"onig's theorem

Simplified approaches to bipartite graph characterization

Enhanced pedagogical value for graph theory

Abstract

We introduce four new elementary short proofs of the famous K\"onig's theorem which characterizes bipartite graphs by absence of odd cycles.